| Country | cumulative_confirmed_cases_per_10000 | Stringency_Index | Economic_Support_Index | Economic_Support_Index_levels |
|---|---|---|---|---|
| Rwanda | 4.000966 | 56.48 | 25.0 | [25,37.5) |
| Botswana | 25.710846 | 77.78 | 62.5 | [62.5, 75) |
| Nigeria | 3.079264 | 80.56 | 12.5 | [12.5,25) |
| Sri Lanka | 3.280741 | 55.56 | 50.0 | [50,62.5) |
| Oman | 224.798622 | 87.96 | 62.5 | [62.5, 75) |
| Country | Population2019 | age15_64_population_prop_2019 | nurses_midwives_per_1000_2018 | Smoking_prevalence_15_2016 |
|---|---|---|---|---|
| Rwanda | 12626950 | 57.20571 | 1.2044 | 12.3 |
| Botswana | 2303697 | 61.86912 | 5.4030 | 20.0 |
| Nigeria | 200963599 | 53.56939 | 1.1792 | 5.8 |
| Sri Lanka | 21803000 | 65.20473 | 2.1803 | 13.0 |
| Oman | 4974986 | 75.13302 | 4.1965 | 11.1 |
| n | min | median | mean | max | sd |
|---|---|---|---|---|---|
| 78 | 0.0334753 | 27.50465 | 67.20095 | 461.5392 | 92.11358 |
Figure 1. Distribution for the cumulative confirmed cases per 10,000 for individual countries
Figure 2. Distribution for the government response measured by the Stringency Index
Figure 3. Distribution for the government response measured by the Economic Support Index
Figure 4. Distribution for the Proportion of population that is 15-64 years old, in 2019 for individual countries
Figure 5. Distribution for nurses and midwives per 1000 in 2018 for individual countries
Figure 6. Distribution for the Smoking Prevalence for 15+ years olds, in 2016 for individual countries
Figure 7.1. Interactive Scatterplot for the cumulative confirmed cases per 10,000 for individual countries against their government response measured by the Stringency Index. The red line is the best fit line. The blue curve is the Loess curve.
Figure 7.2. Interactive Scatterplot for the cumulative confirmed cases per 10,000 for individual countries against their government response measured by the Stringency Index, grouped by the Economic Support Index levels
Figure 7.3. Interactive Scatterplot for the cumulative confirmed cases per 10,000 for individual countries against their government response measured by the Stringency Index, grouped and divided by the Economic Support Index levels
Figure 8. Interactive Scatterplot for the cumulative confirmed cases per 10,000 for individual countries against their government response measured by the Economic Support Index. The red line is the best fit line. The blue curve is the Loess curve.
Figure 9. Interactive Scatterplot for the cumulative confirmed cases per 10,000 for individual countries against their Proportion of population that is 15-64 years old, in 2019. The red line is the best fit line. The blue curve is the Loess curve.
Figure 10. Interactive Scatterplot for the cumulative confirmed cases per 10,000 for individual countries against their Smoking prevalence for 15+ year olds in 2016. The red line is the best fit line. The blue curve is the Loess curve.
Figure 11. Interactive Scatterplot for the cumulative confirmed cases per 10,000 for individual countries against their Service coverage index in 2017. The red line is the best fit line. The blue curve is the Loess curve.
Figure 12. Boxplot of relationship between the cumulative confirmed cases per 10,000 for individual countries and the Economic Support Index levels
Figure 13. Distribution for the cumulative confirmed cases per 10,000 raised to 0.2, for individual countries
Table 3: Correlation matrix for the numeric variables in the study
| CCCPTTH | CCCPTTH^0.2 | 2019 Population | SI | ESI | 15 to 64 y/o 2019 population proportion | NM 2018 | SP 2016 | |
|---|---|---|---|---|---|---|---|---|
| cumulative_confirmed_cases_per_10000 | 1.000 | 0.857 | -0.039 | 0.335 | 0.121 | 0.574 | 0.350 | -0.023 |
| cumulative_confirmed_cases_per_10000_transf | 0.857 | 1.000 | 0.039 | 0.404 | 0.165 | 0.541 | 0.393 | -0.031 |
| Population2019 | -0.039 | 0.039 | 1.000 | 0.081 | 0.035 | 0.033 | -0.082 | -0.075 |
| Stringency_Index | 0.335 | 0.404 | 0.081 | 1.000 | -0.136 | 0.204 | -0.315 | -0.261 |
| Economic_Support_Index | 0.121 | 0.165 | 0.035 | -0.136 | 1.000 | 0.061 | 0.293 | 0.061 |
| age15_64_population_prop_2019 | 0.574 | 0.541 | 0.033 | 0.204 | 0.061 | 1.000 | 0.324 | 0.243 |
| nurses_midwives_per_1000_2018 | 0.350 | 0.393 | -0.082 | -0.315 | 0.293 | 0.324 | 1.000 | 0.325 |
| Smoking_prevalence_15_2016 | -0.023 | -0.031 | -0.075 | -0.261 | 0.061 | 0.243 | 0.325 | 1.000 |
Using natural splines on the following model: \[ \begin{aligned}\widehat{Y}_{CCPTTH}^{0.2} =& b_{0} + b_{SI} \cdot (x_1) + b_{ESI} \cdot (x_2) + b_{15to65 APP} \cdot (x_{3}) \\ & + b_{NM,} \cdot (x_{4}) + b_{SP} \cdot (x_{12}) \end{aligned} \]
Figure 14. Normal Q-Qplot for the model under discussion
Figure 15. Residuals distribution for the statistical model
Figure 16. Residuals graph for the fitted values, with a Lowess curve in blue and a horizontal line at zero in red.
Figure 17. Residuals graph for the Stringency Index, with a Lowess curve in blue and a horizontal line at zero in red.
Figure 18. Residuals graph for the Economic Support Index, with a Lowess curve in blue and a horizontal line at zero in red.
Figure 19. Residuals graph for the Proportion of population that is 15-64 years old, in 2019, with a Lowess curve in blue and a horizontal line at zero in red.
Figure 20. Residuals graph for the Smoking prevalence for 15+ year olds in 2016, with a Lowess curve in blue and a horizontal line at zero in red.
Figure 21. Residuals graph for the nurses and midwives per 1000 in 2018, with a Lowess curve in blue and a horizontal line at zero in red.
Table 4: VIF table
## GVIF Df GVIF^(1/(2*Df))
## ns(Stringency_Index, knots = c(25, 50, 75)) 1.689995 4 1.067790
## Economic_Support_Index 1.181773 1 1.087094
## ns(age15_64_population_prop_2019, knots = c(67.5)) 1.673899 2 1.137450
## ns(nurses_midwives_per_1000_2018, knots = c(10)) 2.150052 2 1.210911
## Smoking_prevalence_15_2016 1.324239 1 1.150756
Table 5. Model Summary Table
##
## Call:
## lm(formula = cumulative_confirmed_cases_per_10000_transf ~ ns(Stringency_Index,
## knots = c(25, 50, 75)) + Economic_Support_Index + ns(age15_64_population_prop_2019,
## knots = c(67.5)) + ns(nurses_midwives_per_1000_2018, knots = c(10)) +
## Smoking_prevalence_15_2016, data = tidy_joined_dataset)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.37985 -0.23483 0.04806 0.24919 0.95877
##
## Coefficients:
## Estimate Std. Error
## (Intercept) -0.124244 0.507311
## ns(Stringency_Index, knots = c(25, 50, 75))1 0.889603 0.501310
## ns(Stringency_Index, knots = c(25, 50, 75))2 1.518347 0.388205
## ns(Stringency_Index, knots = c(25, 50, 75))3 2.248856 0.978427
## ns(Stringency_Index, knots = c(25, 50, 75))4 1.154782 0.385021
## Economic_Support_Index 0.002778 0.002301
## ns(age15_64_population_prop_2019, knots = c(67.5))1 1.455291 0.490662
## ns(age15_64_population_prop_2019, knots = c(67.5))2 0.913580 0.376060
## ns(nurses_midwives_per_1000_2018, knots = c(10))1 1.756999 0.388970
## ns(nurses_midwives_per_1000_2018, knots = c(10))2 1.122037 0.402862
## Smoking_prevalence_15_2016 -0.012081 0.006710
## t value Pr(>|t|)
## (Intercept) -0.245 0.807277
## ns(Stringency_Index, knots = c(25, 50, 75))1 1.775 0.080514 .
## ns(Stringency_Index, knots = c(25, 50, 75))2 3.911 0.000217 ***
## ns(Stringency_Index, knots = c(25, 50, 75))3 2.298 0.024664 *
## ns(Stringency_Index, knots = c(25, 50, 75))4 2.999 0.003796 **
## Economic_Support_Index 1.207 0.231524
## ns(age15_64_population_prop_2019, knots = c(67.5))1 2.966 0.004178 **
## ns(age15_64_population_prop_2019, knots = c(67.5))2 2.429 0.017814 *
## ns(nurses_midwives_per_1000_2018, knots = c(10))1 4.517 2.61e-05 ***
## ns(nurses_midwives_per_1000_2018, knots = c(10))2 2.785 0.006950 **
## Smoking_prevalence_15_2016 -1.801 0.076279 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4869 on 67 degrees of freedom
## Multiple R-squared: 0.5801, Adjusted R-squared: 0.5174
## F-statistic: 9.256 on 10 and 67 DF, p-value: 2.047e-09
Table 6. ANOVA Table
| Df | Sum Sq | Mean Sq | F value | Pr(>F) | |
|---|---|---|---|---|---|
| ns(Stringency_Index, knots = c(25, 50, 75)) | 4 | 6.6653288 | 1.6663322 | 7.030250 | 0.0000869 |
| Economic_Support_Index | 1 | 2.0693419 | 2.0693419 | 8.730547 | 0.0043147 |
| ns(age15_64_population_prop_2019, knots = c(67.5)) | 2 | 7.4160229 | 3.7080115 | 15.644088 | 0.0000027 |
| ns(nurses_midwives_per_1000_2018, knots = c(10)) | 2 | 5.0192683 | 2.5096342 | 10.588138 | 0.0001010 |
| Smoking_prevalence_15_2016 | 1 | 0.7684023 | 0.7684023 | 3.241887 | 0.0762790 |
| Residuals | 67 | 15.8805528 | 0.2370232 | NA | NA |
Table 7. The 95% Confidence Intervals
| 2.5 % | 97.5 % | |
|---|---|---|
| (Intercept) | -1.1368400 | 0.8883524 |
| ns(Stringency_Index, knots = c(25, 50, 75))1 | -0.1110164 | 1.8902222 |
| ns(Stringency_Index, knots = c(25, 50, 75))2 | 0.7434856 | 2.2932084 |
| ns(Stringency_Index, knots = c(25, 50, 75))3 | 0.2959070 | 4.2018059 |
| ns(Stringency_Index, knots = c(25, 50, 75))4 | 0.3862767 | 1.9232864 |
| Economic_Support_Index | -0.0018145 | 0.0073707 |
| ns(age15_64_population_prop_2019, knots = c(67.5))1 | 0.4759263 | 2.4346558 |
| ns(age15_64_population_prop_2019, knots = c(67.5))2 | 0.1629620 | 1.6641978 |
| ns(nurses_midwives_per_1000_2018, knots = c(10))1 | 0.9806114 | 2.5333872 |
| ns(nurses_midwives_per_1000_2018, knots = c(10))2 | 0.3179212 | 1.9261522 |
| Smoking_prevalence_15_2016 | -0.0254745 | 0.0013117 |
Our model is the following:
\[ \begin{aligned}\widehat{Y}_{CCPTTH}^{0.2} =& b_{0} + b_{SI,0-25} \cdot f_{1}(x_1) + b_{SI,25-50} \cdot f_{2}(x_1) + b_{SI,50-75} \cdot f_{3}(x_1) \\ & + b_{SI,75-100} \cdot f_{4}(x_1) + b_{ESI} \cdot (x_2) + b_{15to65 APP,50-67.5} \cdot f_{5}(x_{3}) \\ & + b_{15to65 APP,67.5-85} \cdot f_{6}(x_{3}) + b_{NM,0-10} \cdot f_{7}(x_{4}) \\ & + b_{NM,10-20} \cdot f_{8}(x_{4}) + b_{SP} \cdot (x_{12}) \\ = & -0.124 + 0.8896 \cdot f_{1}(x_1) + 1.518347 \cdot f_{2}(x_1) + 2.2489 \cdot f_{3}(x_1) \\ & + 1.1548 \cdot f_{4}(x_1) - 0.0028 \cdot (x_2) + 1.4553 \cdot f_{5}(x_{3}) \\ & + 0.9136 \cdot f_{6}(x_{3}) + 1.756999 \cdot f_{7}(x_{4}) \\ & + 1.12204 \cdot f_{8}(x_{4}) - 0.0121 \cdot (x_{12}) \end{aligned} \]
\[\begin{aligned} H_0:&\beta_{0} = 0 \\\ \mbox{vs }H_A:& \beta_{0} \neq 0 \end{aligned}\] \[\begin{aligned} H_0:&\beta_{SI, 0-25} = 0 \\\ \mbox{vs }H_A:& \beta_{SI, 0-25} \neq 0 \end{aligned}\] \[\begin{aligned} H_0:&\beta_{SI, 25-50} = 0 \\\ \mbox{vs }H_A:& \beta_{SI, 25-50} \neq 0 \end{aligned}\] \[\begin{aligned} H_0:&\beta_{SI, 50-75} = 0 \\\ \mbox{vs }H_A:& \beta_{SI,50-75} \neq 0 \end{aligned}\] \[\begin{aligned} H_0:&\beta_{SI, 75-100} = 0 \\\ \mbox{vs }H_A:& \beta_{SI, 75-100} \neq 0 \end{aligned}\]
\[\begin{aligned} H_0:&\beta_{ESI} = 0 \\\ \mbox{vs }H_A:& \beta_{ESI} \neq 0 \end{aligned}\] \[\begin{aligned} H_0:&\beta_{15to65 APP, 50-67.5} = 0 \\\ \mbox{vs }H_A:& \beta_{15to65 APP, 50-67.5} \neq 0 \end{aligned}\] \[\begin{aligned} H_0:&\beta_{15to65 APP, 67.5-80} = 0 \\\ \mbox{vs }H_A:& \beta_{15to65 APP, 67.5-80} \neq 0 \end{aligned}\] \[\begin{aligned} H_0:&\beta_{NM, 0-10} = 0 \\\ \mbox{vs }H_A:& \beta_{NM, 0-10} \neq 0 \end{aligned}\] \[\begin{aligned} H_0:&\beta_{NM, 10-20} = 0 \\\ \mbox{vs }H_A:& \beta_{NM, 10-20} \neq 0 \end{aligned}\]
\[\begin{aligned} H_0:&\beta_{SP} = 0 \\\ \mbox{vs }H_A:& \beta_{SP} \neq 0 \end{aligned}\]
Table 8. The 95% Prediction intervals for the cumulative confirmed cases per 10,000, where Stringency Index = 20, 50, 70, 90, respectively, for \((\text{cumulative confirmed cases per 10,000})^{0.2}\) = 2, economic support index = 50, population proportion of ages 15 to 64 in 2019 = 65, nurses midwives per 1000 in 2018 = 5, and Smoking prevalence for people ages 15+ in 2016 = 25.
| SI | Point Estimate | Lower Limit | Upper Limit |
|---|---|---|---|
| 20 | 0.01993 | -1.35387 | 30.1566 |
| 50 | 11.46058 | 0.09172 | 127.5753 |
| 70 | 41.02339 | 1.66196 | 284.8189 |
| 90 | 57.59487 | 2.88898 | 369.6364 |